Oddly, their arachnid is an insect (7)
I believe the answer is:
termite
'an insect' is the definition.
(termite is a kind of insect)
'oddly their arachnid' is the wordplay.
'oddly' indicates alternate letters.
'arachnid' becomes 'mite' (mite is a kind of arachnid).
The alternating letters of 'their' are 'ter'.
'ter'+'mite'='TERMITE'
'is' is the link.
(Other definitions for termite that I've seen before include "Nest-building insect" , "Mound-building insect" , "Social insect" , "Social type" , "Ant-like insect that feeds on wood" .)