With "Bother!" ran off to shelter inside from the storm (7)
I believe the answer is:
tornado
'storm' is the definition.
(tornado is a kind of storm)
'with bother ran off' is the wordplay.
'with' is an insertion indicator.
'bother' is an anagram indicator.
'off' becomes 'todo' (I can't explain this - if you can you should give a lot more credence to this answer).
'ran' with letters rearranged gives 'rna'.
'rna' going into 'todo' is 'TORNADO'.
'to shelter inside from the' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for tornado that I've seen before include "Whirling storm" , "Cyclone, twister" , "Terrible current" , "Windy hazard" , "Destructive wind vortex" .)