“obey.” This is a command.
The phrase “deep respect and trembling” uses two similar ideas to emphasize the importance of honoring their masters. (See: rc://en/ta/man/translate/figs-doublet and rc://en/ta/man/translate/figs-idiom)
Here “trembling” is an exaggeration used to emphasize how important it is that slaves obey their masters. AT: “and fear” or “as though you were shaking with fear” (See: rc://en/ta/man/translate/figs-hyperbole)
“Heart” here is a synecdoche for truely honorable intentions. AT: “with your truely honorable intentions” (See: rc://en/ta/man/translate/figs-synecdoche)
Serve your earthly master as though your earthly master were Christ himself.
“Heart” here is a metonym for “personal convictions.” AT: “who do the will of God from your personal convictions” (See: rc://en/ta/man/translate/figs-metonymy)
“Heart” here is a metonym for one’s “intentions” or “convictions.” AT: “Serve with full conviction, realizing that you serve the Lord and not just people.” (See: rc://en/ta/man/translate/figs-metonymy)