Ask to have it injected into a different vein (6)
I believe the answer is:
invite
'ask' is the definition.
(I've seen this before)
'it injected into a different vein' is the wordplay.
'injected into' means one lot of letters goes inside another.
'a different' indicates anagramming the letters.
'vein' with letters rearranged gives 'inve'.
'it' put inside 'inve' is 'INVITE'.
'to have' is the link.
(Other definitions for invite that I've seen before include "Ask (someone to visit)" , "Ask to one's home in friendly way" , "Ask round" , "Ask for, say comments" , "Draw" .)