Is the following grammatical? "As noted, expenses will raise, thus the increase in assessments." Should rise be used instead of raise, and is 'thus' a subordinate conjunction as used here? Thanks.

Raise is a transitive verb; i.e. you have to raise something. e.g. raise the bar.

Rise is an intransitive verb; i.e. it does not have a direct object. e.g. It rises.

Therefore, it is:

Expenses will rise.
'Expenses will raise' is wrong.

'thus the increase in assessment' is messy. I do not consider thus a conjunction. I would opt for a lengthier reword using:

; as a result,
; therefore,
and cause

or something similar.

The use of 'thus' in this sentence is very dodgy.

Sorry, if it's not the answer you wanted.