Pay vet mostly to turn up, speak and disappear (9)
I believe the answer is:
evaporate
'disappear' is the definition.
(I've seen this in another clue)
'pay vet mostly to turn up speak' is the wordplay.
'pay vet mostly' becomes 'pave' (I can't justify this - if you can you should give a lot more credence to this answer).
'to turn up' is a reversal indicator.
'speak' becomes 'orate' (orating is a kind of speaking).
'pave' reversed gives 'evap'.
'evap'+'orate'='EVAPORATE'
'and' is the link.
(Other definitions for evaporate that I've seen before include "Turn liquid to gas" , "Change from liquid to gas" , "Turn into vapour, lose moisture" , "Dissolve into the air" , "Melt away" .)