Psalm 20:7 New English Translation

⁷Some trust in chariots and others in horses,^[a]
but we^[b] depend on^[c] the Lord our God.

Psalm 20:7 tn Heb “these in chariots and these in horses.” No verb appears; the verb “invoke” is to be supplied from the following line. The convention of backward ellipsis can apply to the final word of the 2nd line, as in this verse. In this case the idea would be that some “invoke” (i.e., trust in) their military might for victory (cf. NEB “boast”; NIV “trust”; NRSV “take pride”). Verse 8 suggests that the “some/others” mentioned here are the nation’s enemies.
Psalm 20:7 tn The grammatical construction (conjunction + pronominal subject) highlights the contrast between God’s faithful people and the others mentioned in the previous line.
Psalm 20:7 tc The LXX translates the verb as μεγαλυνθησόμεθα (megalunthēsometha) “we will boast.” This may reflect another verb, the Hiphil of גָּבַר (gavar), and depends on two letter confusions, ג (gimel) for ז (zayin) and ב (bet) for כ (kaf).tn Heb “we invoke the name of.” The Hiphil of זָכַר (zakhar), when combined with the phrase “in the name,” means “to invoke” (see Josh 23:7; Isa 48:1; Amos 6:10). By invoking the Lord’s name in prayer, the people demonstrate their trust in him.

New English Translation (NET)