How can I change default clipboard register in Vim?

To paste text from the clipboard in Vim, currently I need to type "+p. How can I change or create an alias for register +, for example, to a? So that Vim would paste text from the clipboard when I type "ap. I tried to map register, but no results.

There's no way to map registers in Vim. Mappings are key mappings.

Not an exact solution for your problem but one of the following two ways may be close enough:

1. Set clipboard to unnamedplus. You can alias the unnamed register to the + clipboard register by adding

   :set clipboard^=unnamedplus
   

   to your vimrc. Whenever you paste from the unnamed register, e.g. by p, you will paste from the clipboard instead. See :help clipboard-unnamedplus

2. Map keys for easy clipboard access. Although you cannot map registers, you can map a key to make clipboard access more convenient. With the following mappings

   :nnoremap <Leader>p "+p
   :xnoremap <Leader>p "+p
   

   you can quickly paste from the clipboard using your <Leader> key and p.