Removing fuzz on wool coat

[JosieRosie]

I have a beautiful teal blue coat that I love but I have noticed that it's looking a bit shabby. The bits that get most wear (arms and front of torso) are getting quite bobbly although none of the material is worn. Have tried dry cleaning but it didn't make a difference. Any ideas on making it look a bit fresher?
TIA

Shave it with a disposable razor.

I do this with jumpers and blankets and they come up well.

Thanks GentleOtter

Or one of those battery operated clothing shavers. Quite time consuming but effective.