ctrl-r follwed by the register lets you paste the contents of a register without leaving insert mode.
Ctrl + r" Put from the default register
Ctrl + rd Put from register d
By the way, in vim they’re called “registers” not “clipboards” and the verb is “put”, not “paste”. (Reminder, to get a visual selection into register d, you would use "dy)
Sometimes you are already in vims insert mode, yanked something and want to paste it, instead of leaving insert mode, pasting, and enter insert mode again, type CTRL-O, paste with p, and you get back to insert mode automatically. Works of course for all normal mode commands.