Periodical issues welcome finger food (5)
I believe the answer is:
sushi
'finger food' is the definition.
'sushi' can be an answer for 'food' (sushi is a kind of food). I am not certain of the 'finger' bit.
'periodical issues welcome' is the wordplay.
'periodical issues' becomes 'sus' (I am not sure about this - if you are sure you should believe this answer much more).
'welcome' becomes 'hi' (both are greetings).
'sus'+'hi'='SUSHI'
Can you help me to learn more?
(Other definitions for sushi that I've seen before include "Japanese rice-based dish" , "rice dishes" , "Japanese vinegared rice dish" , "Japanese cuisine" , "Rice and raw fish wrapped in seaweed" .)