Evolve unlocks at league level 18 and it allows to trade a bunch of cards for a few of higher rarity. No gold is needed for this, but you need to have unlocked the higher rarity card to proceed.
|Common||50 to 5||500 to 5||/|
|Rare||/||50 to 5||200 to 1|
|Epic||/||/||20 to 1|
Here are some charts with all the possible evolutions, updated to Horny Tree Friends event (2018-09-14). The sequence the cards are listed is roughly the same in which they appear on SQUAD tab.