A pupil of William Noy, afterwards attorney-general, a Devonian, and born in the law, he rapidly acquired a large practice, both on the Western circuit and at Westminster; he argued a reported case in the King's Bench in 1628 and was appointed Recorder of Plymouth in August 1640.

In December 1640 he was placed on the committee of scrutiny into the conduct of lords-lieutenant of counties, and on that for the discovery of the "prime promoters" of the new "canons ecclesiastical" passed in the recent irregular session of convocation.

[6] In the committee, which sat at Guildhall after the adjournment of the House of Commons which followed the king's attempt to arrest the five members (4 January 1641/2), he made an eloquent speech in defence of parliamentary privilege.

[6] A curious testimony to Maynard's reputation at this time is afforded by a grant made in his favour by parliament in October 1645 of the books and manuscripts of the late Lord Chief Justice Bankes, with liberty to seize them wherever he might find them.

As a politician he was a strict constitutionalist, protested against the first steps taken towards the deposition of the king, and on the adoption of that policy withdrew from the house as no longer a lawful assembly (November 1648).

The jury were afterwards interrogated by the council of state as to the grounds of their verdict, but refused to disclose them, and Maynard thus escaped censure, and on 9 February 1653/4 was called to the degree of serjeant-at-law.

One Cony, a city merchant, had been arrested by order of the council of state for non-payment of taxes, and Maynard, with Serjeants Thomas Twysden and Wadham Wyndham, moved on his behalf in the upper bench for a habeas corpus.

Their argument on the return, 18 May 1655, amounted in effect to a direct attack on the government as a usurpation, and all three were forthwith, by order of Cromwell, committed to the Tower of London; they were released on making submission (25 May).

On the accession of Richard Cromwell he was made solicitor-general, and in parliament, where he sat for Newtown, Isle of Wight, lent the whole weight of his authority as a constitutional lawyer to prop up the Protector's tottering government.

[12] On Richard's abdication and the resuscitation of the Rump Parliament, Maynard took no part in parliamentary business until 21 February 1659/60, when he was placed on the committee for drafting the bill to constitute the new council of state.

With his brother-serjeant, Sir John Glynne, he rode in the coronation procession, on 23 April 1661, behind the attorney and solicitor-general, much to the disgust of Samuel Pepys, who regarded him as a turncoat.

[6] In the debate on Lord Danby's impeachment (December 1678) Maynard showed a regrettable disposition to strain the Treason Act 1351 (25 Edward III) to his disadvantage, maintaining that its scope might be enlarged by retrospective legislation, which caused Swift to denounce him, in a note to Burnet's Own Time, as 'a knave or a fool for all his law.'

On constitutional questions he steered as a rule a wary and somewhat ambiguous course, professing equal solicitude for the royal prerogative and the power and privileges of parliament, acknowledging the existence of a dispensing power, without either defining its limits or admitting that it had none (10 February 1672/3), at one time resisting the king's attempts to adjourn parliament by message from the Speaker's chair (February 1677/8), and at another counselling acquiescence in his arbitrary rejection of a duly elected speaker (10–11 March 1678/1679).

[6] Maynard opened the case against Edward Colman on 27 November 1678, and took part in most of the prosecutions arising out of the supposed popish plot, including the impeachment of Lord Stafford, in December 1680.

Lord Campbell's interesting story of his slipping away to circuit without leave during the debate on the Exclusion Bill in the preceding November, 'upon which his son was instructed to inform him that if he did not return forthwith he should be sent for in custody, he being treated thus tenderly in respect of his having been long the Father of the House' is a sheer fabrication.

[6] Maynard favoured the impeachment of Edward Fitzharris, declared its rejection by the House of Lords a breach of privilege (26 March 1681), and took part in the subsequent prosecution in the king's bench.

In the action for false imprisonment during his mayoralty brought by Sir William Pritchard against the ex-sheriff Thomas Papillon on 6 November 1684, an incident in the conflict after the court took on the liberties of the City of London, Maynard conducted the defence with eminent skill and zeal, though a Jeffreys-ridden jury found a verdict for the plaintiff with £10,000 damages.

Summoned to give evidence on behalf of Oates on his trial for perjury in May 1685, and questioned concerning the impeachment of Lord Stafford, Maynard pleaded total inability to swear to his memory in regard to that matter, and was dismissed by Jeffreys with a sneer at his supposed failing powers.

He supported the bill for declaring the convention a parliament on the very frank ground that a dissolution, owing to the ferment among the clergy, would mean the triumph of the tory party.

Anthony Wood praises his "great reading and knowledge in the more profound and perplexed parts of the law", and his devotion to "his mother the university of Oxon".

As a politician, his moderation and consistency were generally recognised, though for his part in the impeachments of Strafford and Stafford he was savagely attacked by Roscommon in his Ghost of the late House of Commons (1680–1).