Coming up from bar, heading off, I do songs (7)
I believe the answer is:
arising
'coming up' is the definition.
('arise' can be a synonym of 'come up')
'bar heading off i do songs' is the wordplay.
'heading off' means to remove the first letter.
'do songs' becomes 'sing' (I can't explain this - if you can you should believe this answer much more).
'bar' with its initial letter taken away is 'ar'.
'ar'+'i'+'sing'='ARISING'
'from' acts as a link.
Can you help me to learn more?
(Other definitions for arising that I've seen before include "becoming manifest" , "on the horizon" , "Stemming from like committee matters, or getting up" , "occurring" , "Emerging" .)