That depends on your usage. If you wanted to say, for example, "There was a dramatic increase in the Stock Market yesterday", then "increase" is being used as a noun.
However, you could also say "Modern automakers are researching ways to increase fuel consumption in cars", then "increase" is used as a verb.
Increase is a verb
Increment can be a noun and a verb. Noun: the action of increasing. Verb: to increase by steps.
The word augment is a verb. The past tense is augmented.
The word raise is a regular verb. It can also be a noun meaning an increase in pay or salary.
The part of speech for this particular word is a noun.
part of speech
The part of speech for "answer" is a noun.
what part of speech is beneath
adverb
The part of speech for "explicit" is an adjective.
The part of speech for "lecturer" is a noun.
The part of speech for "rapid" is an adjective.
The part of speech of "came" is a verb.