Say you had a yearly review and you asked for a decent raise (to compare you to market value).
Say the manager told you he will talk with the boss and fight for your demands.

After how long without an answer, you'll start looking for another job?

I am waiting for a response over two months now.

I'd ask for an update first but yeah, two month is plenty of time to start searching

@awelxtr I've asked for an update two weeks ago,
He said he was just in a meeting talking about it.

Start searching

I'm always looking. Raise or not if I get offered more money somewhere else I'm taking it.

I asked for a raise in August last year a few weeks went by and the Managing Director said he would come back to me, a few weeks later they said no. December I applied for and was offered another role, I spoke with management about being offered another role they didn’t seem particularly bothered. Handed my notice in BAM 25% pay increase to better what the other company offered and changes to my terms etc. I would have been happy with 10%

I worked on a four week principal between asking and prompting

Agreed with the general consensus so far: look for something else. Having an offer in hand means you'll actually have two options: the offer itself, and more bargaining power with your current employer.

Before taking the offer, you can try a more aggressive approach. Be respectful, and don't burn bridges of course, but you may be able to get a bigger raise if your employer doesn't want to lose you.