Tailless arachnid gives a sign (7)
I believe the answer is:
scorpio
'a sign' is the definition.
(sign of the zodiac)
'tailless arachnid' is the wordplay.
'tailless' means to remove the last letter (the tail of the word is removed).
'arachnid' becomes 'scorpion' (scorpion is a kind of arachnid).
'scorpion' with its final letter taken away is 'SCORPIO'.
'gives' acts as a link.
(Other definitions for scorpio that I've seen before include "7 [SIGN OF THE ZODIAC]" , "star group" , "Zodiac sign like mini-lobster" , "Ford model?" , "Eight sign of Zodiac, of arachnid family" .)