Peter Cosgreave was included in the Navy List of Medical Officers in 1814. 
He was employed as surgeon on the convict ship Friendship in 1817.
The Friendship departed England on 3rd July 1817 and arrived in Port Jackson on 14th January 1818. He and the Master were criticised by the free passengers travelling on the Friendship for their treatment of the female prisoners who were said to have been cruelly punished and left with inadequate water.
Peter Cosgreave married Maria Ford in 1819 at St. Clement's Danes.
In 1833 surgeons Peter Cosgreave, George Drysdale, Richard Hinds and George Shaw Rutherford signed correspondence calling for medical reform which highlighted the difficulties of naval surgeons finding employment in peace time.
A circular written at the time put forward an argument for reform: It is thought that the present is a favourable moment for pressing on Parliament the claims of medical officers in the king's service, to enter into private practise in any part of the British dominions, without being subject to the control of any of the medical corporations.
The peace of 1815 threw out of the public employment a considerable body of naval and military medical practitioners. The interests of themselves and the public demanded, however, that a new field should be opened for their professional exertions; it being material that in the event of new hostilities with any foreign power they should not be found inefficient from want of practice.
They were prevented in this by Charters and Acts of Parliament.
There were thought to be two to three thousands surgeons bound by these restrictive laws. 
Peter Cosgreave died on 16th May 1841 in Norfolk street, Strand. His widow Maria died in December 1861 at the same address.