The Army Lists for 1758, 1761 and 1767 include Chaplain Philip Hughes as Chaplain of 44th Regiment of Foot in America, with seniority from 4 Jan 1752, which I take to be the date that he was appointed chaplain.
The (British) National Archives holds a letter dated 6 Jan 1775 from the Court of St James's from Lord Rochford to Lord Harcourt that the King [George III] is pleased to approve the following appointments "Reverend Mr Thomas St Clair Abercromby to be chaplain of the 44th Foot in room of the Reverend Middleton Cornys Middleton deceased." The document is in SP 63/445 folios 3-4.
https://discovery.nationalarchives.gov.uk/details/r/C20406095The Army List for 1778 lists Chaplain M Cornyn Middleton as Chaplain of the 44th with seniority from 8 July 1768.
From these documents I surmise that Philip Hughes ceased to be chaplain of the 44th between 1767 and July 1768. As you know the Regiment returned from North America to Ireland in 1765 and since Hughes was still listed as being with the Regiment in 1767, I assume that he came back with them and didn't stay in North America. He may, of course, have decided to return of his own accord after leaving the post of chaplain, if he had acquired land in Canada and wanted to settle there.
There are several online histories of the 44th during their time in North America and Canada, but none of them mention Chaplain Philip Hughes. If you want to get an idea of the fighting the Regiment was involved in, probably the best is: Carter, Thomas (1864).
Historical Record of the Forty-Fourth, or the East Essex Regiment of Foot. which is available on
Google books. The fighting in Canada ended with the Treaty of Fontainbleu in 1763.