To hold out or extend a hand or object toward someone; to reach out so it can be taken.
母は赤ん坊におもちゃを差し伸べた。
The mother held out a toy to the baby.
彼は倒れた老人にそっと手を差し伸べた。
He gently reached out his hand to the fallen old man.
若者はお年寄りに荷物を差し伸べた。
The young man handed the luggage to the elderly person.
To thrust a spear or similar weapon toward someone; a forward stabbing/thrusting motion (martial or historical usage).
古武道では相手に槍を差し伸べる型がある。
In classical martial arts there is a form where you thrust a spear at the opponent.
戦いの場で兵士は槍を差し伸べて前進した。
On the battlefield the soldier advanced, thrusting his spear.
To offer help or assistance to someone; to extend support to a person in need (often used as 'to lend a hand').
地震の被害者に多くの国が手を差し伸べた。
Many countries offered assistance to the earthquake victims.
彼女は困っている同僚に差し伸べることで信頼を得た。
She earned trust by offering help to a colleague in trouble.
地元のボランティアが被災地に食料と物資を差し伸べた。
Local volunteers provided food and supplies to the disaster area.