Lavish in support of archaeological work most of all (8)
I believe the answer is:
prodigal
'lavish' is the definition.
('prodigal' can be similar in meaning to 'lavish')
'in support of archaeological work most of all' is the wordplay.
'in support of' becomes 'pro'.
'archaeological work' becomes 'dig'.
'most of' means to remove the last letter.
'all' with its last letter taken away is 'al'.
'pro'+'dig'+'al'='PRODIGAL'
(Other definitions for prodigal that I've seen before include "Grip load (anag.)" , "Improvident" , "This son got the fatted calf" , "Wasteful - gold pair (anag)" , "Recklessly wasteful or extravagant" .)