For slimmers, food almost tasteless, initially, and costing nothing (3-4)
I believe the answer is:
fat-free
'for slimmers' is the definition.
(I've seen this before)
'food almost tasteless initially and costing nothing' is the wordplay.
'initially' suggests taking the first letters.
'and' says to put letters next to each other.
'costing nothing' becomes 'free' (given away for free).
The first letters of 'food almost tasteless' is 'fat'.
'fat'+'free'='FAT-FREE'
(Other definitions for fat-free that I've seen before include "Like many low-calorie foods" , "Far feet (anag)" , "Very low in saturates/unsaturates" , "Lite" , "Containing no greasy substances" .)