精力を傾ける (devote one's energies)

The set phrase 精力を傾ける, literally 'tilt one's energy,' meaning to pour one's energy/effort into something, devote oneself wholeheartedly. 傾ける ('tilt, incline') is used metaphorically for directed devotion — the same image underlies 耳を傾ける ('lend an ear').