List giving a new store a rousing start (6)
I believe the answer is:
roster
'list' is the definition.
(a roster is a list or register)
'a new store a rousing start' is the wordplay.
'a new' is an anagram indicator.
'start' suggests taking the first letters.
The initial letter of 'rousing' is 'r'.
'store' is an anagram of 'roste'.
'roste'+'r'='ROSTER'
'giving' is the link.
(Other definitions for roster that I've seen before include "Duty plan" , "Duty list for sorter" , "Resort (anag)" , "List showing turns of duty" , "Roll" .)