If you just stay vigilant, opportunities will arise naturally.
Literal
Without-carelessness attention [as long as-さえ] do-and-be-[conditional-ば] opportunity [topic-は] naturally arise.
~さえ~ば ('if only, as long as') highlights the minimal sufficient condition — just being attentive is enough. 油断なく negates 油断 ('negligence'). おのずから (自ずから, 'naturally, of itself') is a formal adverb. おれば is a slightly literary conditional of おる.