A fellow having a half of bitter as a chaser (5)
I believe the answer is:
after
'as a chaser' is the definition.
I can't judge whether this defines the answer.
'a fellow having a half of bitter' is the wordplay.
'fellow' becomes 'f' (abbreviation - of a society etc.).
'having' means one lot of letters go next to another.
'a half of' means to take half the letters.
'bitter' cut in half is 'ter'.
'a'+'f'+'ter'='AFTER'
Can you help me to learn more?
(Other definitions for after that I've seen before include "In pursuit of, behind" , "Behind; in quest of" , "Subsequently" , "At a later time or behind" , "since" .)