In verse 12 the Hebrew phrase “the daughter of Tyre” refers to the people of that city (see comments on “the daughter of Zion” in 9.14; “daughter of Babylon” in 137.8). However, by omitting the initial “and” one can take it as a vocative and translate “Tyrian princess” (so Traduction œcuménique de la Bible, New English Bible, New Jerusalem Bible, Biblia Dios Habla Hoy). The explicit reference to Tyre may imply that she was from there. In verse 12b will sue your favor translates “will soften (or, flatter) your face,” that is, will try to gain her favor.
Revised Standard Version connects the opening words of verse 13 with the end of verse 12 (also New Jerusalem Bible). This is possible but not necessary. The Hebrew phrase that Revised Standard Version translates all kinds of wealth may be taken to describe the bride (so Good News Translation; see next verse). But there are considerable difficulties with the Hebrew text as it now stands, and commentators and translations vary widely.
Verses 13-15 describe the bridal procession into the palace; first The princess comes in; Good News Translation “in the palace” translates the Hebrew word “within,” which Revised Standard Version in her chamber takes to be rather the place where the princess was decked. It is better to translate “The princess enters the palace.” “How beautiful she is” translates a phrase which seems to mean “all glorious” (see Revised Standard Version footnote); but the noun is taken by Revised Standard Version to mean “valuable things” (as in Judges 18.21, “goods”). Hebrew Old Testament Text Project understands “all glorious” to mean “the whole glorious (array)” and translates “all glorious, the king’s daughter enters.” New English Bible, with a change of text, gets “In the palace honour awaits her.” The term princess, if translated literally as in Hebrew “daughter of the king,” will in most cases no longer refer to the bride. Therefore in many languages one must say “the woman the king will marry.”
Quoted with permission from Bratcher, Robert G. and Reyburn, William D. A Handbook on the Book of Psalms. (UBS Helps for Translators). New York: UBS, 1991. For this and other handbooks for translators see here .