With that small a kitten, 2 weeks tops and they will at least tolerate
if not love each other. Have a place set up to put the kitten when you
go out or just for a little breaktime for the older cat. It's best to
introduce kitten in small amounts so they can get used to each other.

Did you just put them in the same room together  it is not going to work
you  have them separated for a few days to get used to each other
basically   this is what the older cat is thinking  who is this that just
invaded my territory  and the little one is thinking I ain't going near him
he is mean.

You have to gradual introduce them together put the kitten in another room
and close the door for a couple days of course the kitten needs attention.
they will start smelling each other under the door  there will be hissing
don't punish him for that.  Personally when they start playing with each
other under the door you can let them be together with out watching them.
But right now after a day or two letting the kitten out to explore the house
with you watching won't hurt but watch the older cat to make sure no combat
happens  that means claws out biting not hissing it may take a little bit
but don't get discouraged   When the kitten gets big enough he will give the
older cat a run for its money

Yes. It takes time. Give it a month or two before you decide there's a
problem. Cats need to adjust to changes in their lives. A fifteen year
old cat may find a kitten rather boisterous, so make sure they both
have private areas to retreat to, and they both have "alone time" with
you when they won't be bothered. Seperate them for now and do brief,
supervised visits for short periods of time and then gradually work up
to longer and longer periods of time together. And spoil the older cat
- lots of affection and treats and time with you. The kitten will be
fine - the older cat needs to understand that she isn't being replaced
by this interloper and the kitten needs to understand that this house
is to be shared with the resident cat.