Run into an animal that's alongside (7)
I believe the answer is:
abreast
'alongside' is the definition.
(thesaurus)
'run into an animal' is the wordplay.
'run' becomes 'r' (cricket abbreviation).
'into' indicates putting letters inside.
'an' becomes 'a'.
'animal' becomes 'beast' ('beast' can be a synonym of 'animal'**).
'a'+'beast'='abeast'
'r' inserted into 'abeast' is 'ABREAST'.
'that's' is the link.
(Other definitions for abreast that I've seen before include "Level in line" , "Side by side; keeping pace" , "Alongside one another and facing the same way" , "Level or keeping pace with" , "On a level together" .)