Let no one despise him may be rendered as “Don’t let any person among you look down on him.” They may have been inclined to do so because Timothy was young (see 1 Tim 4.12). Despise is more literally “treat as nothing.”

Speed him on his way: see 1 Cor. 16.6. Speed here does not mean “fast”; it rather refers to “help” (Good News Bible): “you must help him to continue his trip.” Good News Bible‘s “you must” translates a Greek imperative “send him on,” literally “send him forward in peace” (see 7.15).

Expecting him can be rendered as “expecting him to return.”

Brethren probably refers to male fellow workers in this verse. This is the view of New Revised Standard Version (also in verse 12), which elsewhere uses inclusive language as consistently as possible.

Quoted with permission from Ellingworth, Paul and Hatton, Howard A. A Handbook on Paul’s First Letter to the Corinthians, 2nd edition. (UBS Handbook Series). New York: UBS, 1985/1994. For this and other handbooks for translators see here .