Born in Poole, and raised in nearby Corfe Mullen, Goodship joined the AFC Bournemouth academy at the age of 12.

[3] On 20 February 2016, Goodship joined League Two side Yeovil Town on a one-month loan deal,[4] he made his debut later that day as a substitute against Portsmouth.

[9] Following his release from Yeovil, Goodship signed for Southern League Premier Division side Weymouth on a one-year contract.

[14] On 5 June 2021, Brandon Goodship returned to National League side Weymouth on a two-year deal following the expiry of his contract at Southend United.

[15] On 27 June 2022, Goodship joined Southern Football League Premier Division South club Salisbury.