They permit entry to alien overwhelmed by biting arachnids (7)
I believe the answer is:
tickets
'they permit entry' is the definition.
The definition suggests an adverb but the answer is not.
'alien overwhelmed by biting arachnids' is the wordplay.
'alien' becomes 'et' (extraterrestrial).
'overwhelmed by' indicates putting letters inside (inserted letters get absorbed or overwhelmed).
'biting arachnids' becomes 'ticks' (tick is a kind of arachnid. I am not sure about the 'biting' bit.).
'et' put into 'ticks' is 'TICKETS'.
'to' acts as a link.
Can you help me to learn more?
(Other definitions for tickets that I've seen before include "Permits" , "Printed pieces of paper as issued for travellers" , "Notices" , "vouchers" .)