A fairly old-fashioned phrase, 上（うえ）は highlights that something is being done or considered as a result of (A). It may be interpreted as ‘once (A), (B)’, ‘since (A), (B)’, ‘now that (A), (B)’, or ‘as long as (A), (B)’. In these meanings, (B) will always be something that is deemed as either obvious or necessary.
上（うえ） in this phrase is a 名詞（めいし） (noun), and will be attached to the 副助詞（ふくじょし） (adverbial particle) は. This creates a literal meaning that is similar to ‘over and above (A), (B)’. This ‘over and above’ has a similar nuance to ‘with that said’, or ‘all things considered’ in English, and just presents (A) as something that is finalized.
This structure follows verbs in the 普通形（ふつうけい） (standard form).

• 一人（ひとり）暮（ぐ）らしを始（はじ）めた上（うえ）は、家事（かじ）など料理（りょうり）は自分（じぶん）で全部（ぜんぶ）やらなくてはいけない。
  Now that I have started living alone, I must do all the housework and cooking on my own.
• アイルランドに住（す）むと決（き）めた上（うえ）は、アイルランドの文化（ぶんか）などを勉強（べんきょう）しなければならない。
  Now that I have decided to live in Ireland, I must study things such as Irish culture.
• この会社（かいしゃ）の従業員（じゅうぎょういん）として働（はたら）く上（うえ）はきちんと我（わ）が社（しゃ）のルールを守（まも）ってもらわないと困（こま）ります。
  As long as you are working as an employee of this company, we need you to follow our rules.

Due to 上には being quite old-fashioned, expressions like からには or 以上（いじょう）は will be heard more frequently in modern-day Japanese, and will carry a similar meaning.

• ワンちゃんを保護（ほご）すると決（き）めたからには、最後（さいご）まで責任（せきにん）をもって育（そだ）てなくてはいけない。
  Now that you have decided to adopt a puppy, you must take responsibility and raise it until the end.
• 十分（じゅうぶん）な証拠（しょうこ）がない以上（いじょう）は、彼（かれ）を逮捕（たいほ）することができません。
  Since we don’t have sufficient evidence, we can’t arrest him.