If you remove a link to a page that has relevant content, especially if there are keywords in the anchor text, it might have a small negative effect. But adding such a link could have a small positive effect. So I think it probably depends on the link you replace it with.
Generally you will be ok with editing/updating links.
I have seen some rare circumstances where there was trouble. I think this was because the actions made Google think the site was selling links. I do not have enough research on this to say for certain. I can say this is the exception and not very common based on my experience.
I wanted to is there any negative editing a link on page or adding new link on a page?
That's really situational... Adding a link will put another link on the page, which will decrease the PageRank distributed by other links on the page, but how much of an effect that will have depends on how many links there are and whether it's internal or external. If it's internal it will lower the PageRank passed by the other internal links, but also reduce the PageRank passed by the external links, so more PageRank 'stays home' ... If it's external then the internal and external links get decreased the same amount, but the PageRank they are decreased by goes somewhere else.
If there are 100 links on the page and you add one, then it's probably not a big deal, because the overall percentage (amount) each is dropped by is not very much, but if there are only 10 links on the page then the amount each is dropped by is greater.
The change imo should not effect the ranking of the page you are adding the link to, but if it's external it's more likely to have a slightly negative effect the other internal pages you link to from the page.