Strength and peace are not often seen together outside the Christian community. Strength is associated with aggressiveness and domination while peace is seen as a passive and spineless.
Yet the strength God give is not aggressive. It is an enabling to do things that we would not normally be able to do. To hold our tongue when we really want to express our anger; deal with a difficult situation which we would rather avoid; express kindness when usually we would feel apathy. God strengthens us to be people of integrity, wisdom and compassion.
Together with strength he gives us peace, not to concede defeat but to have an inner calm whatever the situation. In John 14:27 Jesus says, "Peace I leave with you; my peace I give you. I do not give to you as the world gives. Do not let your hearts be troubled and do not be afraid." God gifts us with peace but it is reliant on us not allowing our hearts to be troubled and afraid. Otherwise we lose the peace he gives us.
Earlier in the chapter when Jesus also told his disciples not to let their hearts be troubled he added, "You believe in God; believe also in me" (v.1). Peace comes from trusting God and believing his plans will ultimately work out for good in our lives, even if they are uncomfortable in the short term. It's knowing that he will strengthen us to handle whatever we are facing.
Therefore God's strengthening actually enables us to live in peace because whatever comes, we know we are able to cope with it.
Strength and peace – two essentials for a spiritual life and God freely gives them to his people.