He carries Glamdring...
In The Two Towers, Gandalf names his sword when asked to surrender it at Edoras:
'Come, come!' said Gandalf. 'We are all friends here. Or should be; for the laughter of Mordor will be our only reward, if we quarrel. My errand is pressing. Here at least is my sword, goodman Háma. Keep it well. Glamdring it is called, for the Elves made it long ago. Now let me pass. Come, Aragorn!'
The Two Towers Book III Chapter 6: "The King of the Golden Hall"
And, as pointed out by various people in the forum thread Valorum links to in a comment on the question, the sword is called out by the narration at the end of Return of the King, when he and the hobbits return to the Shire:
Then the hobbits suddenly realized that people had looked at them with amazement not out of surprise at their return so much as in wonder at their gear. They themselves had become so used to warfare and to riding in well-arrayed companies that they had quite forgotten that the bright mail peeping from under their cloaks, and the helms of Gondor and the Mark, and the fair devices on their shields, would seem outlandish in their own country. And Gandalf, too, was now riding on his tall grey horse, all clad in white with a great mantle of blue and silver over all, and the long sword Glamdring at his side.
Return of the King Book VI Chapter 7: "Homeward Bound"
How he retains the sword after his death and resurrection is never directly explained, but it doesn't seem like much of a bother; we know that Gandalf was resurrected on Zirakzigil (the same place he died), so it doesn't seem implausible that he could simply have held onto it when Gwaihir picked him up and carried him to Lothlórien.
...but he doesn't appear to ever use it
As Matt Gutting reminds me in comments, although he carries a sword Gandalf doesn't really get a whole lot of use out of it; despite being present at several battles after his resurrection, Gandalf sees practically no combat:
He's absent for much of the Battle of Helm's Deep, but when he does appear he seems to frighten the attackers away without actually fighting any of them:
The hosts of Isengard roared, swaying this way and that, turning from fear to fear. Again the horn sounded from the tower. Down through the breach of the Dike charged the king's company. Down from the hills leaped Erkenbrand, lord of Westfold. Down leaped Shadowfax, like a deer that runs surefooted in the mountains. The White Rider was upon them, and the terror of his coming filled the enemy with madness. The wild men fell on their faces before him. The Orcs reeled and screamed and cast aside both sword and spear. Like a black smoke driven by a mounting wind they fled. Wailing they passed under the waiting shadow of the trees; and from that shadow none ever came again.
The Two Towers Book III Chapter 7: "Helm's Deep"
There's very little fighting during the Siege of Gondor (unlike in the films), and no enemy is inside the city (where Gandalf is) until Grond breaks down the gates. But basically immediately after this, Gandalf is called away to save Faramir, and the battle basically ends while he's in the Houses of Healing
- The only confrontations Gandalf gets into here are against the Witch-king, who leaves without a fight when the Rohirrim arrive, and against Denethor, who Gandalf disarms with magic
Despite being present at the Battle of the Black Gate, neither Gandalf nor Aragorn seem to do any actual fighting:
All about the hills the hosts of Mordor raged. The Captains of the West were foundering in a gathering sea. The sun gleamed red, and under the wings of the Nazgûl the shadows of death fell dark upon the earth. Aragorn stood beneath his banner, silent and stern, as one lost in thought of things long past or far away; but his eyes gleamed like stars that shine the brighter as the night deepens. Upon the hill-top stood Gandalf, and he was white and cold and no shadow fell on him. The onslaught of Mordor broke like a wave on the beleaguered hills, voices roaring like a tide amid the wreck and crash of arms.
Return of the King Book VI Chapter 4: "The Field of Cormallen"
He's not even present at the Scouring of the Shire, having left the Hobbits to clean that one up on their own
