Eve was admitted to practice law in Knox County in 1807 and energetically entered county politics. He became a trustee, like his father-in-law, for the county seat of Barbourville in 1810. He also became a trustee for his church. The county elected him its representative in the Kentucky legislature in 1810, 1811, and 1815. During the War of 1812, he rose to the rank of colonel. After the war, from 1817 to 1821, he served as the Knox County state senator. In 1819 he was president of the Bank of Barbourville. From 1828 to 1836 he was a circuit judge in Kentucky. Often too generous for his own interests, Eve endorsed loans for some of his friends who went bankrupt, leaving him close to losing his own slaves and homestead.
Eve was a supporter of Henry Clay and advocated internal improvements by both state and national governments and high protective tariffs for United States industries; he reluctantly sponsored the national bank as well. As a National Republican and member of the Kentucky electoral college in 1833, he voted for Clay. He then campaigned on behalf of the Whigs and the election of William Henry Harrison to the presidency in 1840. As a reward for his diligent efforts, Eve was appointed chargé d'affaires to the Republic of Texas on April 15, 1841.
He greatly admired Sam Houston and sponsored the annexation of Texas. He toured Texas from Galveston to the new capital, Austin, and was favorably impressed with the productivity of the land. He was fully confident that Mexico could never reconquer Texas. Following Secretary of State Daniel Webster's instructions of June 14, 1841, Eve obtained the ratification of the boundary line surveyed by a joint commission of the Republic of Texas and the United States. Both parties agreed that the line was the Sabine River and, from near the southeast corner of what is now Panola County, the thirty-second parallel north to the Red River. Eve sought to negotiate a new commercial treaty with the Texas government, but disagreement over certain provisions of the convention prevented its acceptance by either side. Further negotiations were soon dropped with the renewal of American interest in the annexation of Texas.
Throughout 1842 Mexican attacks increased, and Texans encouraged Eve to lay the annexation issue before his government. Eve sympathized with the Texans' plight but regarded Houston's response to the attacks, the attempted naval blockade of Mexican ports, as ineffectual. He persuaded Houston to rescind his blockade proclamation since it adversely affected United States and British attempts to end current hostilities. Fearful that financial misery would cause Texas to depend upon some stronger nation, particularly Great Britain, Eve implored President John Tyler not to lose the opportunity to annex the republic. Although willing to acquire Texas, Tyler felt the timing was not right for passing annexation in the Senate. Instead, the president continued to offer the mediation of the United States government with Mexico on behalf of Texas.
Mediation failed, however, on September 11, 1842, when Mexican general Adrián Woll captured and held San Antonio for nine days. The Mexican incursions led Houston to remove the government from Austin to Houston, then to Washington-on-the-Brazos. While the republic had no permanent capital, Eve chose to move the legation archives to Galveston, where he could receive mail from the United States faster and where, he hoped, the sea air would help his tuberculosis.
William S. Murphy replaced Eve on April 3, 1843, as the United States diplomat in Texas. Assistant Secretary of State Fletcher Webster, an ardent anti-annexationist, took the first opportunity to recall Eve for a slight infraction of the rules-Eve had violated his private instructions by drawing an advance upon his salary. During the past winter, Eve and his wife had suffered from bouts of fever. Eve died in Galveston in mid-June 1843 and was buried there. His wife returned to their home in Barbourville, Kentucky.
29° 17.632, -094° 48.676
Trinity Episcopal Cemetery