A challenge keeping close to Jennifer and Dawn (7)
I believe the answer is:
arrival
'dawn' is the definition.
(both can mean the beginning or advent of something)
'a challenge keeping close to jennifer' is the wordplay.
'challenge' becomes 'rival' (rival can mean to challenge or compete with).
'keeping' means one lot of letters goes inside another.
'close to' says to take the final letters (the close/ending of).
The last letter of 'jennifer' is 'r'.
'rival' enclosing 'r' is 'rrival'.
'a'+'rrival'='ARRIVAL'
'and' is the link.
(Other definitions for arrival that I've seen before include "Appearance (at a place)" , "Entry" , "Act of coming" , "Attainment of destination" , "Coming - comer" .)