That’s one way for new alleles to enter a population. Some scientists think they can also be introduced from other sources such as bacteria or viruses.
Yes, recombination can create new alleles. Also, gene flow from other populations. So these three – new mutations, recombination, and gene flow – are the most common ways for a population to acquire new alleles. Horizontal, or lateral, transfer is also a mechanism in prokaryotes (nearly the entire genome of a species of Wolbachia has been found within the genome of Drosophila ananassae – so lots of new genes too, not just alleles).