From Cambridge Dictionary:
Complements are necessary to complete the meaning of a noun.
I think it means "of sth." must follow "a/the sense".
Suppose there is such a context: A boy says, "The stand-up show is so funny. There is a sense of humour." His friends reply, "We all feel the sense" or "We all feel such a sense." Is this response acceptable?
A person has (or doesn't have) a sense of humour. We wouldn't say that a comedy show has one - so, no, the friends' responses are not natural.
In contexts like a sense of despair, the word means something like an awareness, an instinctive feeling. If a person said that they felt a sense of despair, their companion might reply "I feel it too" or "I feel like that too."
