Pirouetting priest in party is slippery (5)
I believe the answer is:
oiled
'slippery' is the definition.
(I've seen this in another clue)
'pirouetting priest in party' is the wordplay.
'pirouetting' says the letters should be written in reverse (pirouette is a spin in ballet - letters spin round).
'priest' becomes 'eli' (biblical figure).
'in' indicates putting letters inside.
'party' becomes 'do' (do is a kind of party).
'eli' inserted within 'do' is 'delio'.
'delio' written backwards gives 'OILED'.
'is' is the link.
(Other definitions for oiled that I've seen before include "Anointed" , "Oldie (anag)" , "Lubricated or drunk" , "tipsy" , "Lubricated (with drink?)" .)