Tight chap is grabbing everything initially (4)
I believe the answer is:
mean
'tight' is the definition.
(synonyms)
'chap is grabbing everything initially' is the wordplay.
'chap' becomes 'man' (chap can mean a man).
'is grabbing' indicates putting letters inside.
'initially' says to take the initial letters.
The first letter of 'everything' is 'e'.
'man' going around 'e' is 'MEAN'.
(Other definitions for mean that I've seen before include "Bad-tempered" , "Type of average" , "Paltry" , "Stingy; five Dn" , "Stingy in average way" .)