Leaders of gardeners' and zoologists' unions meet privately to seek a higher offer (6)
I believe the answer is:
gazump
'seek a higher offer' is the definition.
(as in gazumping someone in an auction)
'leaders of gardeners' and zoologists' unions meet privately' is the wordplay.
'leaders of' suggests taking the first letters.
The first letters of 'gardeners and zoologists unions meet privately' is 'GAZUMP'.
'to' acts as a link.
(Other definitions for gazump that I've seen before include "After agreeing a lower price with one person, accept a higher one from another" , "Raise the price of something after agreeing a lower one" , "Raise price of property after agreeing a lower sum" , "Make late higher bid for house" , "Raise the price of a house after agreeing a lower price" .)