By-products given dubious PR by nobs, heading off (4-4)
I believe the answer is:
spin-offs
'by-products' is the definition.
('spin-off' can be a synonym of 'by-product')
'dubious pr by nobs heading off' is the wordplay.
'dubious pr' becomes 'spin' (spin is a type of PR).
'by' is a charade indicator (letters next to each other).
'nobs' becomes 'toffs' ('toff' can be a synonym of 'nob').
'heading off' means to remove the first letter.
'toffs' with its initial letter removed is 'offs'.
'spin'+'offs'='SPIN-OFFS'
'given' is the link.
(Other definitions for spin-offs that I've seen before include "Incidental benefits" , "By-products or incidental results of larger projects" .)