expression
please treat me well; I look forward to working with you; please remember me
A polite set phrase used when starting a new relationship, such as at work, in a new group, or when asking for future cooperation. It can also be used when parting to ask someone to keep in touch. The exact nuance depends on context: it can mean 'please be kind to me', 'I'm counting on you', or 'let's get along well'.
今日からこの部署で働くことになりました。よろしくお付き合いください。
I'll be working in this department starting today. I look forward to working with you.
新しいプロジェクトチームの皆さん、よろしくお付き合いください。
To everyone on the new project team, I look forward to working with you.
Standard polite phrase using ください. The kanji 付き合い is common.
Variant using the kanji 下さい for ください. Slightly more formal or traditional feel.
A polite phrase combining よろしく (well, appropriately) with お付き合い (honorific form of 付き合い, 'association, relationship') and ください (please). The expression is a fixed social formula.