Eat less, digging in every Tuesday, initially (4)
I believe the answer is:
diet
'eat less' is the definition.
(someone on a diet might eat less)
'digging in every tuesday initially' is the wordplay.
'initially' says to take the initial letters.
The first letters of 'digging in every tuesday' is 'DIET'.
(Other definitions for diet that I've seen before include "Regime followed by slimmer" , "prescribed nourishment?" , "Attempt to shift a few pounds" , "Health food - Council" , "Prescribed selection of foods" .)