v. 1
To celebrate victory with pomp; to rejoice over success; to exult in an advantage gained; to exhibit exultation.
v. 2
To prevail over rivals, challenges, or difficulties.
n. 1
A conclusive success following an effort, conflict, or confrontation of obstacles; victory; conquest.
After being defeated in three previous finals, Roger finally tasted triumph at this year's competition.
n. 2
A magnificent and imposing ceremonial performed in honor of a victor.

Related words

Forms

Plural: triumphs → victories, successes, achievements, conquests…
Past participle: triumphed
e.g. triumphed → exulted, gloried, rejoiced, wallowed…

Triumph or Joy?

Triumph is such joy as results from victory, success, achievement.

J. C. Fernald, English Synonyms and Antonyms (1914)

Use in printed books, per decade from 1850 to 2019.

3 letters: win¹
4 letters: coup¹, crow¹
5 letters: glory², boast¹, gloat¹, exult²
6 letters: wallow²
7 letters: success², victory³, succeed², conquer², mastery³, rejoice², prevail², chuckle², jubilee³, ovation³
8 letters: overcome³, conquest², jubilate
9 letters: happiness³, exuberate
10 letters: attainment³, jubilation⁴, exultation
11 letters: achievement³, celebration⁴

The small number after each word is its number of syllables (glory² = 2 syllables).