にくわえて is a formal grammar pattern in Japanese that is a combination of に, and the て-from of the る-Verb 加（くわ）える ‘to add’, or ‘to append’. Often, this structure will be translated as ‘in addition to (A), (B)’, or ‘not only (A), but also (B).
Being that it is a formal phrase,
に加（くわ）えて will also often appear in its formal-conjunctive form
に加（くわ）えて.
To use
にくわえて, simply place it directly after the noun that you would like to highlight as being the base information, before discussing what exactly is ‘in addition’ to that base in the following clause.
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今日（きょう）は暑（あつ）さに加（くわ）えて湿度（しつど）も高（たか）くなる恐（おそ）れがあるので外（そと）に出（で）る方（かた）は熱中症（ねっちゅうしょう）に気（き）をつけてください。
Today, in addition to the heat, there is a threat of high humidity, so please be careful of heat stroke if you are planning to leave the house.
今学期（こんがっき）から文法（ぶんぽう）に加（くわ）えて漢字（かんじ）も教（おし）えることになった。
Starting this semester, in addition to grammar, I will also be teaching Kanji.
彼（かれ）は空手（からて）に加（くわ）えて、剣道（けんどう）もできるそうだ。
I heard that he does kendo in addition to karate.
Both the kanji and hiragana forms of this structure are fairly common, so it will be beneficial to remember both.
Caution -
にくわえて is frequently used when (B) is something that is in addition to (A) in respect to magnifying what was already true of (A). This just means that it will often be used to highlight something being brought about by (B) that would not be possible with just (A) by itself. This increase may be either positive or negative.
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今年（ことし）の母（はは）の日（ひ）には母（はは）に花束（はなたば）に加（くわ）えて心（こころ）を込（こ）めて書（か）いた手紙（てがみ）を渡（わた）すつもりだ。
This Mother's Day, I plan to give my mother a heartfelt letter in addition to a bouquet of flowers.
今年（ことし）になってから電気代（でんきだい）に加（くわ）えてガス料金（りょうきん）までもが高（たか）くなった。
This year, in addition to the electricity bill, even the gas bill has increased.