heiter
cheerful
Describes a person who is cheerful, in a good mood, and carefree.
Trotz des schlechten Wetters war ihre Stimmung heiter und ausgelassen.
Despite the bad weather, her mood was cheerful and exuberant.

cheerful / clear
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cheerful
Describes a person who is cheerful, in a good mood, and carefree.
Trotz des schlechten Wetters war ihre Stimmung heiter und ausgelassen.
Despite the bad weather, her mood was cheerful and exuberant.

The meaning of 'heiter' (cheerful/clear/serene) depends strongly on the noun it describes. If you are talking about a person, it means 'fröhlich' (cheerful). In connection with the weather, it means 'sonnig und klar' (sunny and clear). If it describes a situation, it means 'gelassen und unbeschwert' (calm and carefree).
Mein Großvater ist ein sehr heiterer Mensch.
My grandfather is a very cheerful person.
When a person is being described, 'heiter' (cheerful) is often combined with nouns that describe character or mood. Typical phrases are 'ein heiteres Gemüt haben' (to have a cheerful disposition) or 'von heiterer Natur sein' (to be cheerful by nature).
Sie ist für ihr heiteres Gemüt bekannt und lacht sehr viel.
She is known for her cheerful disposition and laughs a lot.
When 'heiter' (cheerful) describes a person, it often sounds somewhat elevated or literary. It describes a quiet, inner cheerfulness and serenity.
Der heitere Ausdruck auf seinem Gesicht beruhigte alle Anwesenden.
The cheerful expression on his face reassured everyone present.
In weather forecasts, the phrase 'heiter bis wolkig' (clear to cloudy) is a very common fixed expression. It describes a day when sun and clouds alternate.
Die Vorhersage für das Wochenende ist heiter bis wolkig bei 20 Grad.
The forecast for the weekend is clear to cloudy at 20 degrees.
clear
'klar' and 'heiter' can both describe the weather or the sky. 'klar' emphasizes that visibility is good and that little or nothing is clouding the sky. You can also speak of 'klares Wasser' (clear water) or 'klare Luft' (clear air). In weather, 'heiter' mainly means sunny and with few clouds. Learners may confuse the words because a 'heiterer Himmel' (clear/sunny sky) often also seems 'klar'. When it is about good visibility or transparency, 'klar' fits. When it is about pleasant, sunny weather, 'heiter' is more precise.

Für morgen meldet der Wetterbericht heiteres Wetter mit wenigen Wolken.
The weather forecast predicts clear weather with few clouds for tomorrow.
Nach dem Regen war die Luft klar, und man konnte die Berge sehen.
After the rain, the air was clear, and you could see the mountains.