A person convicted of a serious offence can be refused the right to hold public office and in some cases is not able to hold the office at all.
For example, on conviction of indictable offence, you can not be a member of the South Australian Parliament or fill a casual vacancy in Local Councils in South Australia [see s 17(h) and s 31(h) Constitution Act 1934 (SA); s 54(1)(i) Local Government Act 1999 (SA)]. Under the Local Council (Elections) Act 1999 (SA) a person who has been sentenced to imprisonment and is, or could on the happening of some contingency become, liable to serve the sentence or the remainder of the
sentence can not be elected as a councellor [s 17(3)(c)].
If you have been convicted of any offence punishable under the law of the Commonwealth or of a State by imprisonment for one year or longer then you are not able to run as a candidate for Federal Parliament [s 44 Commonwealth of Australia Constitution Act (Cth)].
Loss of right to vote in Federal elections
Under section 93(8) of the Commonwealth Electoral Act 1918 (Cth), a person who is serving a sentence of imprisonment for an offence punishable by imprisonment of more than three years loses the right to vote in Federal elections, although there is no loss of voting rights in State elections.