Arrive having entered favourite in race (7)
I believe the answer is:
compete
'race' is the definition.
The definition and answer can be both related to competing as well as being verbs in their base form.
Maybe you can see an association between them that I can't see?
'arrive having entered favourite' is the wordplay.
'arrive' becomes 'come' (coming is a kind of arriving).
'having' means one lot of letters goes inside another.
'entered favourite' becomes 'pet' (I can't justify this - if you can you should give a lot more credence to this answer).
'come' enclosing 'pet' is 'COMPETE'.
'in' is the link.
Can you help me to learn more?
(Other definitions for compete that I've seen before include "Struggle for victory" , "Take part (in race)" , "Take part in hope of winning" , "Contend, vie" , "Contend (for a prize)" .)