Under the management of Rory Gallagher, Parke received a call-up to the Donegal senior football panel in late 2014.[8] He started Gallagher's first match in charge, a 2015 Dr McKenna Cup away defeat to Derry.[9] He is a former under-21 player for the county football team.[10][11]
^ abCraig, Frank (1 October 2020). "St Eunan's finally looking to 'Parke' 48 years of hurt". Donegal News. p. 58. The 26-year-old already has two SFC medals for the Black and Amber at home and he's picked up a string of titles hurling for his county at various grades… Parke says St Eunan's now see themselves very much as a dual club.
^ abFerry, Ryan (17 May 2019). "Hurlers rise to Christy Ring challenge". Donegal News.
^"Christy Ring cup round up". Irish Independent. Independent News & Media. 13 May 2019. Retrieved 13 May 2019. Gary Hughes netted a hat-trick as Wicklow defeated Christy Ring debutants Donegal in Letterkenny… Donegal – P Burns; Conor Parke, C McDermott, M Callaghan; J O'Loughlin, S McVeigh, S Gillespie; J Boyle, D Cullen; R McDermott, C Matthewson, C Finn; G Browne, L Henderson, D Duffy. Subs: C Flood for Finn (42), R Hilferty for Henderson (46).