It is the 連用中止法 (i-stem) version of 切る.
Since doing (...)
〇〇してその後ずっと〇〇していない。 after 〜たverb＋ , きり is primarily used to show that some time has passed since performing some action, and you have not done it since. In almost every situation, (A) is something that has only happened once, and きり can be interpreted as 'ever since'.
晩ご飯食べたきり何も食べてないから、めちゃお腹が空いた。 Since eating dinner, I have not eating anything. therefore, my stomach is super empty.
10ヶ月前に日本に出たきり、帰国していない. Since leaving japan 10 months ago, he has not returned to his home country.
卒業したきり、会ってない。 Since graduating, we haven't met.
Only (...)
similar to だけ, but putting more emphasis. Also withnoun＋ andcounter it can mean 'only'.
一人きりになれる時間が欲しい。 I want some time for myself alone.
彼とは一度きりしか会えていない。 I was only able to meet him once.
Only doing (...)
他のことをしないで、〜たけしている A combination of the "only" and the "since" meaning. 寝たきり is a very often used expression.
お祖母ちゃんは去年病気で倒れて、寝たきりになった。 Since grandma fell sick last year, and she became bedridden (**can only lie in bed)
階段で転んで、寝たきりになってしまった Since falling from the stairs, the only thing I have been able to do was lie in bed.
夫が入院したので、つきっきりで{看病|かんびょう}した。 When my husband was in the hospital, the only thing I did was take care of him (I did nothing else).
赤ちゃんのお世話にかかりっきりで、掃除も洗濯もできない All I have been doing was taking care of the baby, so I have not been able to do laundry or cleaning.
Casual
っきり is thecasual variant of きり.
ふたりっきりですね。 It's just the two of us, isn't it?
Youtube: Game Gengo - N3 grammar #12
https://bunpro.jp/grammar_points/きり
Youtube: 日本語の森 - だけ vs のみ vs きり