Increase rate of backing favourites and ahead (4,2)
I believe the answer is:
step up
'increase rate' is the definition.
'step up' can be an answer for 'increase' (stepping up is a kind of increasing). I'm not certain of the 'rate' bit.
'backing favourites and ahead' is the wordplay.
'backing' says the letters should be written in reverse.
'favourites' becomes 'pets' ('pet' can be a synonym of 'favourite').
'and' is a charade indicator (letters next to each other).
'ahead' becomes 'up' (similar in meaning).
'pets' in reverse letter order is 'step'.
'step'+'up'='STEP-UP'
'of' is the link.
Can you help me to learn more?
(Other definitions for step up that I've seen before include "Sudden increase (in rate, output, etc)" , "Raise by stages" , "Boost" , "Advancement (on a ladder or career)" , "Accelerate - promotion" .)