You may
exertTo exert a permanent, you choose to have it not untap during your next untap step.
A permanent can be exerted even if it’s not tapped or has already been exerted in a turn. If you exert a permanent more than once before your next untap step, each effect causing it not to untap expires during the same untap step.
An object that isn’t on the battlefield can’t be exerted.
“You may exert [this creature] as it attacks” is an optional cost to attack (see rule 508.1g). Some objects with this static ability have a triggered ability that triggers “when you do” printed in the same paragraph. These abilities are linked. (See rule 607.2h.) (CR 701.43) this creature as it attacks. When you do, it gets +1/+0 and gains
first strikeFirst strike is a static ability that modifies the rules for the combat damage step. (See rule 510, “Combat Damage Step.”)
If at least one attacking or blocking creature has first strike or double strike (see rule 702.4) as the combat damage step begins, the only creatures that assign combat damage in that step are those with first strike or double strike. After that step, instead of proceeding to the end of combat step, the phase gets a second combat damage step. The only creatures that assign combat damage in that step are the remaining attackers and blockers that had neither first strike nor double strike as the first combat damage step began, as well as the remaining attackers and blockers that currently have double strike. After that step, the phase proceeds to the end of combat step.
Giving first strike to a creature without it after combat damage has already been dealt in the first combat damage step won’t preclude that creature from assigning combat damage in the second combat damage step. Removing first strike from a creature after it has already dealt combat damage in the first combat damage step won’t allow it to also assign combat damage in the second combat damage step (unless the creature has double strike).
Multiple instances of first strike on the same creature are redundant. (CR 702.7) until end of turn. (An exerted creature won't
untapTo untap a permanent, rotate it back to the upright position from a sideways position. Only tapped permanents can be untapped. (CR 701.26) during your next
untapTo untap a permanent, rotate it back to the upright position from a sideways position. Only tapped permanents can be untapped. (CR 701.26) step.)