Woman priest to speak and vanish (9)
I believe the answer is:
evaporate
'vanish' is the definition.
(I've seen this before)
'woman priest to speak' is the wordplay.
'woman' becomes 'eva' (woman's name).
'priest' becomes 'p' (ecclesiastical abbreviation).
'to speak' becomes 'orate' (orating is a kind of speaking).
'eva'+'p'+'orate'='EVAPORATE'
'and' is the link.
(Other definitions for evaporate that I've seen before include "let off steam" , "Vaporise" , "Go from liquid to vapour" , "Desiccate, dry up" , "Turn from liquid to vapour" .)