dnd 5e – Is there a way for the character of an adventure league in the eighth season to acquire a heavy armor competition?

There are certain divine domains of clerics that provide the heavy armor domain as a class feature ("bonus domain"), which means that it does not need to appear in the multiclass competition table (PHB, page 164). See this question for more information about that.

Bonus skill
When you choose this domain in the first level, you gain ability with heavy armor.

Life Domain (PHB, page 60) is one of those examples of the PHB, but there are others (but whether or not you can have permission to choose some of them can depend on which books are allowed with your "PHB + 1"). Depending on the domain you choose, you could also master the martial weapon.

This also means that only a multiclass level will "cost" you to get that armor skill, with no need to spend any ASI on feats like Heavily Armored (unless you need to use the ASI to achieve certain skill scores, see below. .)

Note that, according to the multi-classification requirement in PHB, p. 163, you must have an Intelligence score of at least 13 (which I assume you will have as an assistant) for multiclass outside of assistant, and a Wisdom score of at least 13 to multiclass inside cleric…

Also keep in mind that your cleric spells would be based on Wisdom, not Intelligence, so, unless you have the same Intelligence and Wisdom scores (at the time of writing, you have not indicated your character's skill scores) , your cleric spells would probably be a little less powerful than your wizard spells (for example, with regard to how high your spell attack bonus and DC is to save spells). But a magician who is capable of healing is always good to have …

dnd 5e – Is there any way for the character of an adventure league in the eighth season to acquire a heavy armor competition?

There are certain divine domains of clerics that provide the heavy armor domain as a class feature ("bonus domain"), which means that it does not need to appear in the multiclass competition table (PHB, page 164).

Life Domain (PHB, page 60) is one of those examples of the PHB, but there are others (but some of them may depend on the books that are allowed with their "PHB + 1").

This also means that you will only "cost" a level multiclass to get that armor skill.