So there is an attempt after a bit of hesitation (4)
I believe the answer is:
ergo
'so' is the definition.
('ergo' can be a synonym of 'so')
'an attempt after a bit of hesitation' is the wordplay.
'an attempt' becomes 'go' (go is a kind of attempt).
'after' means one lot of letters go next to another.
'a bit of hesitation' becomes 'er' (what a hesitating person might say).
'go' after 'er' is 'ERGO'.
'there is' acts as a link.
(Other definitions for ergo that I've seen before include "'Cogito, ---- sum'" , "Hence" , "Thus" , "It follows" , "as a consequence" .)