Following service in the Second World War with the South Wales Borderers, Eagar was appointed as captain and secretary of Hampshire in 1946.

Following the end of his playing career, Eagar commentated on cricket matches for BBC Radio and Southern Television.

[5] As a part-time slow left-arm orthodox bowler, he took 16 wickets at a bowling average of exactly 33;[6] it was for Oxford that he took his only five-wicket haul in first-class cricket, with figures of 6 for 66 against Sussex at Eastbourne in 1939.

[7] In addition to representing Oxford in cricket, Eagar also played field hockey for the university, for which he gained a blue.

[2] During the summer break in 1938 and 1939, Eagar continued to play for Gloucestershire in the County Championship, making an additional fifteen appearances.

[5] Eagar served in the Second World War, having been commissioned as a second lieutenant onto the general list whilst still a student at Oxford in August 1938.

[8] He joined the South Wales Borderers in October 1939,[9] and was an instructor at Cowley Barracks for part of the war, alongside future British Army Lieutenant-General James Wilson.

[14] Two years into his secretaryship, he convinced pre-war professional Arthur Holt to coach Hampshire after his playing career had ended.

[2] Running concurrently with his Hampshire career, Eagar also made first-class appearances for the South in the 1946 North v South fixture, for the Over-33s against the Under-33s in 1949, for the Marylebone Cricket Club (MCC) in 1952 and 1958 (playing his final first-class match for the MCC against Oxford University), and for the Duke of Norfolk's XI;[3] the latter consisted of three appearances against Jamaica on a tour of that country in March 1957, with Eagar captaining and managing the team during the tour.

He was succeeded as Hampshire captain by Colin Ingleby-Mackenzie, who Eagar had identified him as "the man to inspire a mixed bag of cricketers beyond their promise".

[24] In August 1958 he did some cricket commentary for BBC Radio in the South and West of England only,[25] and in 1960 he commentated for Southern Television.