Psalm 119:49 is the kind of hope we find in all those who long for redemption, who long for God to make God’s glory present, and who yearn for justice. In fact, people like Mary and Simeon and Anna — from Luke’s first two chps — are the kind for whom this prayer is so characteristic. Here it is:
Remember your word to your servant,
in which you have made me hope.
Two points: First, it is likely (in my mind) that the hope here follows from disappointment after the previous section (vv. 41-48). The hopes of those verses — deliverance, answers, walking about at ease, and not being ashamed before the royals — evidently did not materialize.

The psalmist’s response is not to say: if God doesn’t answer my (emphasis) prayers, God must not care; maybe even God doesn’t exist. No, this psalmist presses on further. Request, request not granted, expression of hope and confidence in God, request again.
Second, the psalmist calls God to “remember” (zakar). God can remember sins; God can remember promises. Thus, “remember” here does not mean recall or memory; instead, it means “to remember in such a way as to bring that promise to pass.” Zechariah’s name, you may know, means “YHWH remembered.” A good example of all of this is Hannah saying God remembers her by giving to her a baby (1 Sam 1:11, 19). Thus, Exodus 32:13: “Remember Abraham, Isaac, and Israel, your servants, how you swore to them…”
Both Mary and Zechariah connect the conceptions of their children to God’s remembering of the covenant with Abraham.
To summon God to remember is to call on God to glorify himself by establishing the promise.