Eviston made his
League of Ireland debut for
Home Farm at Tolka Park on 2 November 1975. On 7 August 1976, Home Farm played
Everton in a pre season friendly at
Goodison Park. Twenty years later the same club provided the opposition in Eviston's testimonial. In 1978, he joined
Bohemians and was their top scorer in the league in 1980/81 with 9 goals from 20 games (1 as substitute). In total he played 110 league games (99 plus 11 as sub) scoring 31 league goals. He made a scoring debut for Bohs on 10 September 1978. He made 6 appearances in European competition for Bohs against
AC Omonia and
Dynamo Dresden in the
1978–79 European Cup and
Sporting Clube de Portugal in the
1979–80 UEFA Cup. On 30 April 1980, he represented the League of Ireland against Argentina at the River Plate Stadium where
Diego Maradona scored in a 1–0 defeat and on 3 September 1981 Terry was part of a League of Ireland side that played Brazil in Maceió. During that season he was the club captain at Dalymount. His last game for Bohs was the 1983
FAI Cup Final loss. After five seasons at
Dalymount Park, Rovers new manager
Jim McLaughlin (footballer) signed Terry in July 1983. In his first season at
Milltown, Rovers won the League for the first time in twenty years. After 2 goals in 25 total appearances Terry transferred to
Athlone Town A.F.C. in November 1984. He made his debut at Sligo on the 18th and until he signed for Dundalk in the summer of 1986 he played in all 43 league games in that period. In his seven years at
Oriel Park, he won the League twice, the
FAI Cup once and the
League of Ireland Cup twice and won the Soccer Writers' Personality of the Year award in 1987–88. He was also Player of the Month in March 1988. He also made 6 appearances in European competition for Dundalk against
AFC Ajax in the
1987–88 European Cup Winners' Cup, against
Red Star Belgrade in the
1988–89 European Cup and
Budapest Honvéd FC in the
1991–92 European Cup. In the
1990–91 League of Ireland season, Eviston was everpresent in the league scoring 10 goals as Dundalk won the league on the last day at Cork with Eviston playing a role in Tom McNulty's winner. He rejoined Rovers in the summer of 1993 and scored 6 goals in 25 appearances as he picked up his fourth League medal in his first season back in the Hoops. He made one appearance for Rovers in the
1994–95 UEFA Cup. His last game for Rovers was the final game of the
1995–96 League of Ireland season. In May 1996, a
League of Ireland XI played Everton in Eviston's testimonial at Dalymount Park. He won an Irish amateur cap against Greece in 1978 and an Olympic cap against Hungary in 1986. His 101st and last League of Ireland goal was the winner for Cobh against Galway United on 20 September 1997. Cobh goalkeeper
Nicky Byrne saved a penalty to ensure the home side their first win of that season. At the end of the
2012 League of Ireland season, Newe is joint forty first in the all-time League of Ireland goalscoring list with 101 league goals Eviston was naturally left footed and brave in the air, a proficient crosser with close control. His versatility shone through as he played outside left, striker and left back. Passionate and the ultimate team player his goal celebrations were always memorable. ==Management career==