Keen Sight. The eagle has advantage on Wisdom (Perception) checks that rely on sight.
Conduit. The thunderbird can grant resistance to lightning damage to anyone riding it.
Storm Bringer. The thunderbird’s innate spellcasting ability is Wisdom (DC 16 save). The thunderbird can innately cast the following spells, requiring no material components:
At Will: feather fall, gust of wind, thunderwave
3/day: call lightning, wind wall
1/day: control weather
Multiattack. The thunderbird makes two attacks: one with its beak and one with its talons.
Beak. Melee Weapon Attack: +5 to hit, reach 5 ft., one target. Hit: 14 (2d6 + 5) piercing damage.
Talons. Melee Weapon Attack: +5 to hit, reach 5 ft., one target. Hit: 17 (2d10 + 5) slashing damage.
Description
The thunderbird is a large, avian creature. A close relative of the phoenix, the thunderbird can create storms as it flies and is highly sensitive to danger.
Thunderbirds bring the storm on their wings. In times of drought, they are welcomed with joy and celebration. In other times, they are placated with gifts in hopes that they might leave quickly before flooding begins. When angered, thunderbirds can call down hurricanes and lay waste to entire villages, so in regions where these birds dwell, many villages maintain extensive rituals designed to appease and honor the local thunderbirds.
Thunderbirds nest near the base of waterfalls, where the constant thrum of crashing water prepares the hatchlings for a life at the heart of a storm. Once the chicks have hatched, their parents carry the offspring to nests at the top of mountains, where the young are struck by their first bolts of lightning and learn the mysteries of the storm.
Based on its stats, you might want to change the attack rolls to +7 unless it's supposed to not be proficient with its own beak and talons. Also, the average damage for those attacks should be 12 and 16 respectively. Otherwise, that's a fine monster ya got there.