Meaning of "approval rally"
If you read the whole article, you will see that ‘rally’ is used in the sense of recovery. The recovery is in Trump’ “approval ratings”, which had reached a low ebb.
Had I been editing, I should have suggest replacing the ambiguous ‘rally’ (given Trump’s notorious propensity for holding huge public rallies) with the unambiguous word - the more so since vast hordes of readers limit themselves to scanning the headlines.