Reserved; shy or very considerate — describes someone who is modest and reluctant to assert themselves.
彼は遠慮深い性格で、会議ではあまり意見を言わない。
He is reserved and doesn't speak up much in meetings.
遠慮深い妻は、ごちそうをすすめられても遠慮してしまった。
A reserved wife declined the offer of food out of politeness.
遠慮深い態度は礼儀正しく見えるが、時には率直さが必要だ。
Being reserved can look polite, but sometimes frankness is necessary.