No, but there is an alternative.
You can't forget a spell and have it be replaced with a new spell in your spellbook. You can erase,burn, or rip a spell from your spell book if you like however, and will have to spend time, effort and coin to fill that space. (Spell books only have 100 pages.) (Basic Rules v0.1, page 49.)
There are two ways besides gaining levels to add spells to your spellbook. One is by adventuring, and finding old scrolls.
You might find other spells during your adventures. You could discover
a spell recorded on a scroll in an evil wizard’s chest, for example,
or in a dusty tome in an ancient library.
Adding these scrolls to your spellbook costs 50 gp and 2 hours per level of the spell. (You can also copy spells you already know for 10gp and 1 hour per level.)
(Basic Rules v0.1, page 32.)
Another method which is alluded to but not spelled out is by using the downtime system after discussing it with your DM. Downtime works in days, and you must spend at least 8 hours a day working on what you are trying to do. In this case, you'll be visiting a school of wizardry or a university, or an old magic shop, or meeting with an old wise wizard as a mentor.
While learning new skills, languages, and tools are explicitly mentioned as things you can do during downtime, learning new spells is not, therefore it currently falls under this paragraph:
Downtime activities other than the ones presented below are possible.
If you want your character to spend his or her downtime performing an
activity not covered here, discuss it with your DM.
(Basic Rules v.01, page 68)